We proposed a mathematical model of flow and extrusion in the 3D printing process (FDM technology). The model is based on fluid mechanics and uses conservation laws taking into account friction losses and local resistance losses. We performed a parametric study of the model. We have obtained experimental data on the rheology of compositions based on bimodal powders containing micro- and nanoparticles. The rheological properties of low-filled mixtures of powders with polymer differ from those of highly-filled mixtures of bimodal powders. These data are used as the basis for calculating the extrusion rate of compositions in FDM 3D printing of the considered compositions. The results of calculations of the extrusion rate depending on temperature, pressure, and dispersion of powders are given in the report. The search for optimal printing parameters based on mathematical modeling of the process is the goal of this work.